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it to discriminate between the 'exceedingly numerous' possible
combinations presented (how, Poincare does not say) for its
inspection, and calmly saying that the 'subconscious' rejects a|l
but the 'useful' combinations because it has a feeling for sym-
metry and beauty, sounds suspiciously like solving the initial
problem by giving it a more impressive name. Perhaps this is
exactly what Poincare intended, for he once defined mathe-
matics as the art of giving the same name to different things; so
here he may be rounding out the symmetry of his view by giv-
ing different names to the same titling. It seems strange that a
man who could have been satisfied with such a 'psychology* of
mathematical invention was the complete sceptic in religious
matters that Poincare was. After Poincare's brilliant lapse into
psychology sceptics may well despair of ever disbelieving
During the first decade of the twentieth century Poincare^ s
fame increased rapidly and he came to be looked upon, espe-
cially in France, as an oracle on all things mathematical. His
pronouncements on all manner of questions, from politics to
ethics, were usually direct and brief, and were accepted as final
by the majority. As almost invariably happens after a greart
man's extinction, PoincarS's dazzling reputation during his
lifetime passed through a period of partial eclipse in the decade
following his death. But his intuition for what was likely to be
of interest to a later generation is always justifying itself. To
take but one instance of many, Poincare was a vigorous oppo-
nent of the theory that all mathematics can be rewritten in
terms of the most elementary notions of classical logic; some-
thing more than logic, he believed, makes mathematics what it
is. Although he did not go quite so far as the current intuitionist
school, he seems to have believed, as that school does, that at
least some mathematical notions precede logic, and if one is to
be derived from the other it is logic which must come out of
mathematics, not the other way about. Whether this is to be
the ultimate creed remains to be seen, but at present it appears
as if the theory which Poincare assailed with all the irony at Ms
command is not the final one, whatever may be its merits*
Except for a distressing illness during his last four years